The post Logic Seminar talk: Julia Robinson, existential definability, and Hilbert’s 10th problem appeared first on Institute for Logic and Data Science.

]]>**Title**: Julia Robinson, existential definability, and Hilbert’s 10^{th} problem

**Abstract**: Julia Bowman Robinson put forward in 1952 her notions of *existential definability* and *exponential growth*, both regarding relations on natural numbers. She foresaw that one of the new century problems posed by David Hilbert in the year 1900 would be settled by singling out an exponential-growth, existentially definable relation. The problem in question called for an algorithm that would establish, for any given polynomial *P* with integer coefficients, whether the equation *P = 0* has integer solutions or not.

Julia Robinson’s outlook had a decisive influence in the research that led, almost twenty years later, to a proof of the algorithmic unsolvability of Hilbert’s 10^{th} problem. She had designed from the outset a scheme for getting a specification of exponentiation in polynomial terms, out of any alike specification of an exponential-growth relation. In a 1969 paper, she would propose an improved version of her reduction scheme, of which a possible further refinement shines through a 1975 paper that she wrote in collaboration with Yuri V. Matiyasevich.

By retracing the stages of Julia Robinson’s contribution to the existential definition of exponentiation, this seminar does not simply intend to pay homage to an outstanding scientist. From an in-depth revisitation of her studies on Hilbert’s 10^{th}, along with the contributions of Martin Davis and Yuri Matiyasevich, a novel characterization of a key concept in computability might emerge: that of a *listable *set.

The talk will be online; people are welcome to join us physically at FMI Hall 214 “Google”.

**Google Meet link**: https://meet.google.com/xwm-syvx-bbr

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]]>The post Logic Seminar talk: A notational extension of classical first-order logic to deal with vague language appeared first on Institute for Logic and Data Science.

]]>**Title**: A notational extension of classical first-order logic to deal with vague language

**Abstract**: Vague language is treated as statistical dispersion, using the interplay of preference relations and monadic predicates. A notational extension of classical first-order logic allows defining a tolerant and a strict predicate for each monadic predicate. Results include the failure of weak non-contradiction and of a weak law of excluded middle, and the validity of weak tolerance principles. The logic proposed is compared to other order-sorted logics.

The talk will take place physically at FMI Hall 214 “Google”.

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]]>The post Logic Seminar talk: Possibility theory and the arithmetic of fuzzy numbers appeared first on Institute for Logic and Data Science.

]]>**Title**: Possibility theory and the arithmetic of fuzzy numbers

**Abstract**: Taking inspiration from the seminal work in probability theory by A. N. Kolmogorov and H. R. Pitt, we intend to lay a sound foundation for fuzzy arithmetic, which is based on possibility theory beside fuzzy logic. A possibilistic interpretation of fuzzy arithmetic has long been known, however without taking it to its full consequences: in this paper we stress the basic role of the two limit-cases of possibilistic interactivity, namely deterministic equality versus non-interactivity, thus getting rid of weak points which have so far enfeebled more traditional approaches to fuzzy arithmetic.

The talk will take place physically at FMI Hall 214 “Google”.

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]]>The post Logic Seminar talk: Lean-certified Dynamic Epistemic Logic with Actions for Security Protocols appeared first on Institute for Logic and Data Science.

]]>**Title**: Lean-certified Dynamic Epistemic Logic with Actions for Security Protocols

**Abstract**: We define a complete system of epistemic propositional dynamic logic with actions, that is fully defined and certified with the proof assistant Lean. Within our system, we specify security protocols as sequence of actions and we use epistemic reasoning for analyzing their properties.

The talk will take place physically at FMI Hall 214 “Google”.

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]]>The post New Project: Common Representation for Normative Statements and Research Results appeared first on Institute for Logic and Data Science.

]]>An early demo of a small-scale pilot project may be found here.

For more information, see the project page.

The post New Project: Common Representation for Normative Statements and Research Results appeared first on Institute for Logic and Data Science.

]]>The post Logic Seminar talk: On a theorem of Gallai and related questions appeared first on Institute for Logic and Data Science.

]]>**Title**: On a theorem of Gallai and related questions

**Abstract**: A theorem was stated by Tibor Gallai without proof and was later proven by several authors, in particular E. Witt or R. Rado. The theorem says that for every *k*-coloring of ℤ^{n} and every finite subset *F*⊆ℤ^{n}, there exists a homothetic image of *F* which is monochrome. This fact suggests various ultimately unsolvable sequences of SAT instances.

The talk will take place physically at FMI Hall 214 “Google”.

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]]>The post Project in collaboration with Runtime Verification: Matching Logic and Lean appeared first on Institute for Logic and Data Science.

]]>The project marks the start of our partnership with Runtime Verification (RV), and concerns the Lean formalization of Matching Logic (ML), a unifying logic for program specification and verification introduced by RV founder and CEO Grigore Roșu and his collaborators, which also serves as the theoretical foundation of the 𝕂 Semantic Framework. The project goals are to enhance the ML ecosystem by adding Lean support and to ultimately offer the 𝕂 ecosystem a trusted interactive formal verification environment.

For more information, see the project page.

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]]>The post Logic Seminar talk: On the Expressiveness of a Logic of Separated Relations appeared first on Institute for Logic and Data Science.

]]>**Title**: On the Expressiveness of a Logic of Separated Relations

**Abstract**: We compare the model-theoretic expressiveness of the existential fragment of Separation Logic over unrestricted relational signatures (SLR) with only separating conjunction as logical connective and higher-order inductive definitions, traditionally known as the symbolic heap fragment, with (Monadic) Second Order Logic ((M)SO). While SLR and MSO are incomparable on structures of unbounded treewidth, it turns out that SLR can be embedded in SO, in general, and that MSO becomes a strict subset of SLR, when the treewidth of the models is bounded by a parameter given as input. We also discuss the problem of defining a fragment of SLR that is equivalent to MSO over models of bounded treewidth. Such a fragment would then become the most general Separation Logic with a decidable entailment problem, a key ingredient of practical verification methods for self-adapting (reconfigurable) component-based and distributed systems. Joint work with Florian Zuleger (TU Wien).

The talk will take place at FMI Hall 214 “Google”; it will also be transmitted online as usual.

**Google Meet link**: https://meet.google.com/xwm-syvx-bbr

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]]>The post Proof Mining Seminar talk: On the Borel-Cantelli Lemmas, the Erdős–Rényi Theorem, and the Kochen-Stone Theorem appeared first on Institute for Logic and Data Science.

]]>On July 13, 2022 at 16:00 EEST, Paulo Oliva (Queen Mary University of London) will give a talk in the Proof Mining Seminar.

**Title**: On the Borel-Cantelli Lemmas, the Erdős–Rényi Theorem, and the Kochen-Stone Theorem

**Abstract**: In this talk we present a quantitative analysis of the first and second Borel-Cantelli Lemmas and of two of their generalizations: the Erdős–Rényi Theorem, and the Kochen-Stone Theorem. We will see that the first three results have direct quantitative formulations, giving an explicit relationship between quantitative formulations of the assumptions and the conclusion. For the Kochen-Stone theorem, however, we can show that the numerical bounds of a direct quantitative formulation are not computable in general. Nonetheless, we obtain a quantitative formulation of the Kochen-Stone Theorem using Tao’s notion of metastability.

**Google Meet link**: https://meet.google.com/xwm-syvx-bbr

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]]>The post Logic Seminar talk: Dedukti appeared first on Institute for Logic and Data Science.

]]>**Title**: Dedukti, a standard language for the interoperability of proof systems

**Abstract**: Dedukti is a logical framework to encode various logics to allow interoperability of proofs between different formal tools, like Coq, PVS or Isabelle. This logical framework is based on λΠ-calculus modulo theory, a λ-calculus with dependent types, and extended with rewriting rules.

After a presentation of the λΠ-calculus modulo theory, I will talk about translations to Dedukti, as well as interoperability challenges.

Finally, I will mention other work done by Deducteam.

The talk will take place at the Runtime Verification Bucharest headquarters (Popa Tatu 18); it will also be transmitted online as usual.

**Google Meet link**: https://meet.google.com/jps-xnmf-yoi

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